A memorandum of understanding between the Shinnecock Indians of Southampton and Nassau County executives on using all or part of the site for a gaming facility is close to completion, a tribal source told The Post.

The tribe said it would prefer not to host gaming on its Hamptons reservation and offered to settle a pending claim on thousands of pricey East End acres in exchange for off-site gaming rights.

Such a deal would be a jackpot for residents of the summer playground of the rich and famous — who have been whining about traffic jams and other problems they believe the facility would cause.

Emboldened by their federal recognition as a tribe last June, the Shinnecocks hope to establish a casino in Nassau and one closer to their reservation.

Possible sites for the Suffolk County facility include a parcel in Yaphank and Brookhaven Airport in Shirley.

The tribe is also factoring into its plans the new racino that will soon open at Aqueduct, next to JFK Airport.

As of now, that facility will be able to take bets only on horses and video slots.

The Post has learned of back-channel discussions between the Shinnecocks and Genting International, Aqueduct’s operator, about a possible joint operation of the Long Island and Queens facilities.

The federal regulations that would govern a Shinnecock facility allow for table games.

“Why would someone drive out to Suffolk County if they can hop over to Aqueduct?” said a member of the Suffolk County Gaming Task Force. “That is playing into their thinking here.”

Genting denied holding talks with the Shinnecocks.

But even if the memorandum is signed by both sides, it’s still not a sure thing.

It would be only the first step in a sale of all or part of the 77-acre coliseum parcel to the Shinnecocks. The National Hockey League’s Islanders would not necessarily be left in the cold — they might also get a facility on the site.

The tribe would still face a series of legal hurdles before the dice could roll.

To host gaming off reservation land, a parcel must first be placed into a trust by the federal government. Only four off-reservation casinos have ever been approved nationally, and a Supreme Court decision last year bars tribes recognized after 1934 from having land placed into trusts.

The Shinnecocks have lobbied President Obama to take action on that restriction.

The tribe would also have to successfully negotiate a gaming compact with the state that would specify, among other things, Albany’s take from the gambling.

A high state official told The Post the proposed agreement appears iffy, because both the legislature and the governor would have to sign off.

And, the official said, the feds are unlikely to take non-Indian land and turn it into Indian land.

That problem derailed the proposed Indian casino in the Catskills — and that had gotten legislative approval.